The Gravity Of Math

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The Gravity of Math

Author : Steve Nadis
Publisher : Basic Books
ISBN 13 : 154160430X
Total Pages : 211 pages
Book Rating : 4.5/5 (416 download)

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Book Synopsis The Gravity of Math by : Steve Nadis

Download or read book The Gravity of Math written by Steve Nadis and published by Basic Books. This book was released on 2024-04-16 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rest. In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world? The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.

Newton's Gravity

Author : Douglas W. MacDougal
Publisher : Springer Science & Business Media
ISBN 13 : 1461454441
Total Pages : 442 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Newton's Gravity by : Douglas W. MacDougal

Download or read book Newton's Gravity written by Douglas W. MacDougal and published by Springer Science & Business Media. This book was released on 2012-12-16 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Newton’s Gravity” conveys the power of simple mathematics to tell the fundamental truth about nature. Many people, for example, know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But very few can explain exactly how and why that happens. Fewer still can calculate the actual pulls of the Moon and Sun on the oceans. This book shows in clear detail how to do this with simple tools. It uniquely crosses disciplines – history, astronomy, physics and mathematics – and takes pains to explain things frequently passed over or taken for granted in other books. Using a problem-based approach, “Newton’s Gravity” explores the surprisingly basic mathematics behind gravity, the most fundamental force that governs the movements of satellites, planets, and the stars. Author Douglas W. MacDougal uses actual problems from the history of astronomy, as well as original examples, to deepen understanding of how discoveries were made and what they mean. “Newton’s Gravity” concentrates strongly on the development of the science of orbital motion, beginning with Galileo, Kepler, and Newton, each of whom is prominently represented. Quotes and problems from Galileo’s Dialogs Concerning Two New Sciences and particularly Newton’s Principia help the reader get inside the mind of those thinkers and see the problems as they saw them, and experience their concise and typically eloquent writing. This book enables students and curious minds to explore the mysteries of celestial motion without having to know advanced mathematics. It will whet the reader’s curiosity to explore further and provide him or her the tools (mathematical or physical) to do so.

The Shape of Inner Space

Author : Shing-Tung Yau
Publisher : Il Saggiatore
ISBN 13 : 0465020232
Total Pages : 398 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Shape of Inner Space by : Shing-Tung Yau

Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

How to Fall Slower Than Gravity

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691185026
Total Pages : pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis How to Fall Slower Than Gravity by : Paul J. Nahin

Download or read book How to Fall Slower Than Gravity written by Paul J. Nahin and published by Princeton University Press. This book was released on 2018-11-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar kind of glass called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

Lost in Math

Author : Sabine Hossenfelder
Publisher : Basic Books
ISBN 13 : 0465094260
Total Pages : 277 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis Lost in Math by : Sabine Hossenfelder

Download or read book Lost in Math written by Sabine Hossenfelder and published by Basic Books. This book was released on 2018-06-12 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this "provocative" book (New York Times), a contrarian physicist argues that her field's modern obsession with beauty has given us wonderful math but bad science. Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

How to Fall Slower Than Gravity

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691229171
Total Pages : 318 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis How to Fall Slower Than Gravity by : Paul J. Nahin

Download or read book How to Fall Slower Than Gravity written by Paul J. Nahin and published by Princeton University Press. This book was released on 2021-11-23 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging collection of intriguing problems that shows you how to think like a mathematical physicist Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar material called NASTYGLASS—and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers—who will need only to have studied advanced high school math and physics—in expanding their mathematical thinking to make sense of the curiosities of the physical world. The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics—including algebra, trigonometry, geometry, and calculus—can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements. More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.

The Shape of a Life

Author : Shing-Tung Yau
Publisher : Yale University Press
ISBN 13 : 0300245521
Total Pages : 449 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis The Shape of a Life by : Shing-Tung Yau

Download or read book The Shape of a Life written by Shing-Tung Yau and published by Yale University Press. This book was released on 2019-02-19 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist

Gravitational Force of the Sun

Author : Pari Spolter
Publisher : Orb Books
ISBN 13 : 9780963810717
Total Pages : 272 pages
Book Rating : 4.8/5 (17 download)

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Book Synopsis Gravitational Force of the Sun by : Pari Spolter

Download or read book Gravitational Force of the Sun written by Pari Spolter and published by Orb Books. This book was released on 2014-12-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correct interpretation of Kepler's third law is Gravitational force is equal to acceleration times the area: F = a .A. It is shown that the sequential mean distances of the planets from the center of the sun follow an exponential law, concluding that gravitation is quantized. New explanation and equation for eccentricity are presented. English translation of Foucault's papers on the pendulum and on the gyroscope

Gravity

Author : James B. Hartle
Publisher : Cambridge University Press
ISBN 13 : 1009051334
Total Pages : 610 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Gravity by : James B. Hartle

Download or read book Gravity written by James B. Hartle and published by Cambridge University Press. This book was released on 2021-06-24 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Renowned relativist James Hartle's fluent and accessible physics-first introduction to general relativity uses minimal new mathematics and begins with the essential physical applications. This ground-breaking text, reissued by Cambridge University Press, makes this fundamental theory accessible to virtually all physics majors.

Gravitation

Author : Charles W. Misner
Publisher : Princeton University Press
ISBN 13 : 0691177791
Total Pages : 1332 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Gravitation by : Charles W. Misner

Download or read book Gravitation written by Charles W. Misner and published by Princeton University Press. This book was released on 2017-10-24 with total page 1332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers

Gravity, a Geometrical Course

Author : Pietro Giuseppe Frè
Publisher : Springer Science & Business Media
ISBN 13 : 9400753608
Total Pages : 346 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Gravity, a Geometrical Course by : Pietro Giuseppe Frè

Download or read book Gravity, a Geometrical Course written by Pietro Giuseppe Frè and published by Springer Science & Business Media. This book was released on 2012-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book, divided in two volumes, is a rich resource for graduate students and those who wish to gain a deep knowledge of the subject without an instructor. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume. Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, “Supergravity and Superstrings” and “The N=2 Wonderland”, He is also the author of a popular science book on cosmology and two novels, in Italian.

From Falling Apples to the Universe

Author : John R Laubenstein
Publisher : Palmetto Publishing
ISBN 13 : 9781649905970
Total Pages : 348 pages
Book Rating : 4.9/5 (59 download)

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Book Synopsis From Falling Apples to the Universe by : John R Laubenstein

Download or read book From Falling Apples to the Universe written by John R Laubenstein and published by Palmetto Publishing. This book was released on 2021-05-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: We all encounter gravity every day, but most people have little understanding of what gravity actually involves. We learned about Newton in high school, but that interpretation is not a complete description of gravity. However, those interested in the subject quickly learn that the math used in our modern explanation of gravity (General Relativity) is overwhelming, suggesting that gravity can only be truly understood by highly trained scientists and mathematicians. The author rejects that notion. He believes gravity can be understood by all and can be scientifically explained using words in lieu of the complicated math. Gravity is a significant force around us, therefore our understanding of it is important to make sense of the universe in which we all live. The universe is constantly changing, and those changes that are not fully understood inﬂuence what we think we see when we look far away-to the past. This book offers a unique path for exploring gravity and gravitation and introduces exceptional ways to think about the subject. Each aspect of gravity and gravitation is clearly explained, and the reader is guided through every step as ideas are developed into scientific models. These models are then used to explore how gravity and gravitation may have shaped the universe. The book has a potential audience far beyond students and academic environments. The author's goal is to provide a real science book that is of interest to the general reader but will also hold the interest of experts in the ﬁeld.

Physics for Mathematicians

Author : Michael Spivak
Publisher :
ISBN 13 : 9780914098324
Total Pages : 733 pages
Book Rating : 4.0/5 (983 download)

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Book Synopsis Physics for Mathematicians by : Michael Spivak

Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:

General Relativity for Mathematicians

Author : R.K. Sachs
Publisher : Springer Science & Business Media
ISBN 13 : 1461299039
Total Pages : 302 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis General Relativity for Mathematicians by : R.K. Sachs

Download or read book General Relativity for Mathematicians written by R.K. Sachs and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).

Gravity, a Geometrical Course

Author : Pietro Giuseppe Frè
Publisher : Springer Science & Business Media
ISBN 13 : 9400754434
Total Pages : 466 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Gravity, a Geometrical Course by : Pietro Giuseppe Frè

Download or read book Gravity, a Geometrical Course written by Pietro Giuseppe Frè and published by Springer Science & Business Media. This book was released on 2012-10-24 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume Two is covers black holes, cosmology and an introduction to supergravity. The aim of this volume is two-fold. It completes the presentation of GR and it introduces the reader to theory of gravitation beyond GR, which is supergravity. Starting with a short history of the black hole concept, the book covers the Kruskal extension of the Schwarzschild metric, the causal structures of Lorentzian manifolds, Penrose diagrams and a detailed analysis of the Kerr-Newman metric. An extensive historical account of the development of modern cosmology is followed by a detailed presentation of its mathematical structure, including non-isotropic cosmologies and billiards, de Sitter space and inflationary scenarios, perturbation theory and anisotropies of the Cosmic Microwave Background. The last three chapters deal with the mathematical and conceptual foundations of supergravity in the frame of free differential algebras. Branes are presented both as classical solutions of the bulk theory and as world-volume gauge theories with particular emphasis on the geometrical interpretation of kappa-supersymmetry. The rich bestiary of special geometries underlying supergravity lagrangians is presented, followed by a chapter providing glances on the equally rich collection of special solutions of supergravity. Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, “Supergravity and Superstrings” and “The N=2 Wonderland”, He is also the author of a popular science book on cosmology and two novels, in Italian.

A Mathematical Introduction To General Relativity

Author : Amol Sasane
Publisher : World Scientific
ISBN 13 : 9811243794
Total Pages : 500 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis A Mathematical Introduction To General Relativity by : Amol Sasane

Download or read book A Mathematical Introduction To General Relativity written by Amol Sasane and published by World Scientific. This book was released on 2021-08-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

The Road to Reality

Author : Roger Penrose
Publisher : Vintage
ISBN 13 : 0593315308
Total Pages : 1136 pages
Book Rating : 4.5/5 (933 download)

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Book Synopsis The Road to Reality by : Roger Penrose

Download or read book The Road to Reality written by Roger Penrose and published by Vintage. This book was released on 2021-06-09 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: **WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin